A regular hexagon is inscribed in a circle. A circle is inscribed into

| September 19, 2021 | education

A regular hexagon is inscribed in a circle. A circle is inscribed into it, into which a regular triangle is inscribed. Find the radius of the larger circle if the side of the triangle is 1 cm.

Determine the radius of the smaller circle in which the regular triangle is inscribed.

r = OH = a * √3 / 3, where a is the side of the triangular.

r = OH = 1 * √3 / 3 = √3 / 3 cm.

A regular hexagon is described around a circle with a radius of √3 / 3 cm. Then the radius of the inscribed circle in a regular hexagon is: r = OH = b * √3 / 2, where b is the side of the hexagon. b = AB = 2 * OH / √3 = (2 * √3 / 3) / √3 = 2 cm.

The radius of the circumscribed circle around a regular hexagon is equal to the side length of this hexagon. R = AB = 2 cm.

Answer: The radius of the larger circle is 2 cm.



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